A single-phase load consists of 12 ohms of resistance in series with 5 ohms of inductive reactance. Impedance equals the square root of the sum of the squares of resistance and reactance, and power factor equals resistance divided by impedance. What is the power factor of this load?
- A0.42
This divides reactance by resistance, which is the tangent of the phase angle rather than the power factor. The power factor is the cosine of that angle.
- 0.92
- C1.08
A power factor greater than one is impossible; it would mean the load consumes more real power than the source supplies. The error is inverting the ratio to impedance over resistance.
- D0.38
This divides reactance by impedance, which gives the reactive factor rather than the power factor. Power factor always uses the resistive side over the hypotenuse.
Why B is correct
Because resistance and reactance are 90 degrees apart, they combine as the sides of a right triangle: 12 and 5 give a hypotenuse of 13 ohms. Power factor is the ratio of the resistive side to the hypotenuse, so 12 divided by 13 gives 0.92 lagging.
What this question is testing
Tests whether you can combine resistance and reactance correctly using the right triangle relationship rather than adding them, and whether you know that power factor is the ratio of resistance to impedance rather than any of the other ratios available in the same triangle.
On the job
The practical payoff is understanding why a clamp meter and a voltmeter multiply out to more volt-amperes than a wattmeter reads on the same circuit. Motors, transformers, solenoids and ballasts all present inductive reactance, and the difference between the two readings is what utilities charge large customers for. It also explains why conductors and overcurrent devices are sized on current, which reflects apparent power, not on the watts the load actually converts.
Memory technique
Three, four, five and twelve, five, thirteen: the impedance triangle loves the same numbers a framer does.
Exam tip
Draw the right triangle: resistance on the bottom, reactance up the side, impedance across. Power factor is bottom over hypotenuse.
Where to look it up
Impedance and power factor are theory, but they explain why Code load calculations are done in volt-amperes rather than watts throughout Article 220.